Determine b so that f(x) is continuous if O 8 x + 6 xS 6 f( x ) = D O 2 x2 + bx +10 x > 6 b =

Q: f is continuous iff f-1(E) is closed

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Q: Find c such that the function 10 г c - || 26 х > с is continuous everywhere. c =

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Q: Let f(x)=ln(2−x2). Find all values of c in the open interval (−1,1) such that f′(c)=0.

A: Here given function Since the is differentiable in the interval (-1, 1) then it is also continuous…

Q: If f(0) = 0 and f"(x) exists for all x>0, then show that %3D f(x) f'(x) xf"(5), 0 < § < x. Also…

A: Let's find.

Q: What is the value of k so that the function f(x) is continuous at x=2 O-3 O - 3/2 1/2 0 1 T-2k f(x)…

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Q: Consider f(x) = 3|x|, which is in R[-2, 2]. a. Find a continuous function F(x) such that F'(x) =…

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Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: Let f(x)=x2+2x. Find all values of c in the interval [−2,0] such that f′(c)=0.

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Q: Find c such that the function f(エ) 8x- 20 I > C is continuous everywhere.

A: NOTE: Refresh your page if you can't see any equations. . find the left-hand limit of the function…

Q: The range of F in F(x) = 2 sin x; - < x< 2 T is: %3D -2SF(x)SO F(x)S2 ) -2SF(x)S2 O O

A: Given:- F(x)=2 sinx  ,-π/2 &lt;x &lt;2π To find:- Range of F(x)

Q: The f(x) 6x2 -5x-4 2x2 +x is discontinuous %3D at x = -1/2. By redefine = w , then f will be…

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Q: Define f: [0,2]-R by f(x) = x²+2x-1 , then the sup f- inf f is : [0,2] [0,2] 1.a O V8 b 0 3.cO 8 dO

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Q: Let f(x) = x³ – 6x ln x + 6x + 1000. Find all x-coordinates of the inflection points. O x = -1 and x…

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Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and g(2x)dx = 3. %3D 2 Find æg(3x²)dx.

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Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: Consider the piecewise function: |x- 1| x² – 1' x <1 f(x) = (Ax² + 6, x 2 1 For what real number A…

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Q: The value of k that makes x2 – kx + 2x – 2k f(x) x # -2 x + 2 4, continuous at x = -2 is x = -2 O 2…

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Q: 8. Consider the function f(x)=/25-x² . a. Find the linearization L(x) of f(x) at x=3.

A: Given expression is , fx=25-x2 to find out the linearization L(x) of f(x) at x=3.

Q: Show that f (x) = 1 − |x| satisfies the conclusion of the MVT on [a, b] if both a and b are positive…

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Q: Let f, g:R R defined by if x 1 (x2 and g(x) = 3x + 2. %3D Find f-1 and g-1.

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Q: Find c such that the function Sx2 – 4 - 4 x c is continuous everywhere. c =

A: Here, the given function is: f(x)=x2-4, if x≤c10x-29, if x&gt;c To find the value of c such that the…

Q: Let f(x) =x² t2X. Find all the values of ċ in the interval [2,0] such that f (c) =0.

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

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Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x&lt;0   So,…

Q: Show that f(x1, x2) = 2 - (x1 - 1)^2 - e^x2^2 is concave.

A: the given function is fx1,x2=2-x1-12-ex22 To find the function is concave we have to show all its…

Q: of of and ду For the function f(x,y) = In (7x + 9y), find

A: The given function,     f(x,y)=ln7x+9y

Q: Find the linearization L(x) at x= a. f(x) = 2x° + 5x - 3 a= 3 L(x) =

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Q: The function f(x) =x + 1/x is concave upward on none O (-1) O (0,) O (0,1) O (1,)

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Q: 2. Find the constant a such that the function is continuous on the entire real number line x2- a2 w…

A: If it is continuous at x=a , then left and right limit must be same at x=a

Q: Determine whether the function 2х + 1 f(x) %3D 2r2 2x2 – x – 1 is continuous: a. at 2; b. at 1.

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Q: Prove, if f(x)= V1+x² –In +1+ 1 is increasing and concave on x X E (0;+∞) .

A: f is increasing if first derivative is positive in the interval  and f has concave if second…

Q: 3. Let f (x) = x ² + 8x + 14. Find all the values interral C-G ,2) such that f (c) = 0 of ċ in the

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Q: what is the antiderivative F(x) of f(X) = 3x1/2-x-1 that satisfies the condition  F(4)= 0? A,…

A: The given function is fx=3x12-x-1 that satisfies the condition F4=0. Find the antiderivative of Fx.

Q: Find the function f(x) such that f' (x) = x²e# with f(0) = 0. O (x² - 2x - 2)e* + 2 O (x2 + x + 2)e*…

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Q: Consider the function xe* if x < 0 g(x) = x³ – 2x2 + x if 0 < x < c , %3D if x 2 c where c is a…

A: Given,gx = xex                            if x≤0x3 - 2x2 + x          if 0&lt;x&lt;c1x…

Q: Suppose that ƒ(x) = x2 and g(x) = | x | . Then thecompositions( ƒ ∘ g)(x) = | x | 2 = x2 and (g ∘…

A: Given: The composite of the two functions are given as,

Q: 2. Suppose that f is a measurable function satisfying m({r €R: [f(x)| 2n}) < ne N. n3' Is f…

A: Given that f is a measurable function, with the following condition satisfied. m(x∈ℝ:…

Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: Find the value of c such that the function is continuous on the entire real number line. f(x)=…

A: Topic = Functions

Q: The absolute maximum of y =-x + 2x +3 on the interval [0, 3] occurs at Select one: O a. None of…

A: Simply take the derivative and equate to zero than solve for x.

Q: Find c such that the function ² - 4 x c is continuous everywhere.

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Q: 1. Determine whether k(x) is continuous at r = 3, where %3D x + 3, x 2.

A: Given  k(x)=x+3,  x&lt;0x2+1, 0≤x≤22x,   x&gt;2 To check the continuity we can use the graph as…

Q: Which values of C makes r(x) (a) left-continuous, (b) right-continuous (c) continuous x2 +3 for x 2

A: If the function r(x) is left-continuous, then use limx→-1-rx=limx→-1+rx, to determine the value of…

Q: ) The domain of the function y = In(1 – x²) is R – [-1,1].

A: Log (x) is defined for every  x is positive real number .

Q: a) Suppose that f(x) = 4x if x<-1 = cx + d if – 1<x< 2 = -5x if x 2 2 Find values of c and d such…

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Q: If the function f (x) = } 6x – 4, x5 is continuous at x =5, then the value of k is %3D %3D O a. 10 O…

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Q: Let g(x) = x2 – 4/x2 – 3x -10 Determine x-value(s) for which g is not continuous

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Q: For what values of h and k is h+2x , 15 x52 -2 < x<-1 2< * 2 - Continuous at every x ? 2x2 - 2x-4,…

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Q: Find c such that the function x c is continuous everywhere. x² – 8 f(x) = {

A: ANSWER : c = 5